A similar wire connector of the mentioned type is known in the art from German reference DE 37 11 675 Al. Herein, cable wires of a pair of wires are placed into the guide channels of a lower housing section and are then pressed into the cutting/clamping contact elements of the lower housing section by means of the crosspieces of a first upper housing section. Cutting-off of the cable wires may be effected by separating knives disposed in the lower housing section. Thereafter, the cable wires of a second pair of wires are placed into the corresponding guide channels of the lower housing section and are pressed into the cutting/clamping contact elements of the lower housing section by means of the crosspieces of a second upper housing section. According to this reference, cutting-off of the cable wires can also be effected by separating knives disposed in the lower housing section. It is disadvantageous, herein, that different housing sections are required, namely the lower housing section forming the guide channels and receiving the cutting/clamping contact elements and possibly the separating knives and the two cover-type upper housing sections with the crosspieces for pressing the cable wires into the cutting/clamping contact elements of the lower housing section. The prior art wire connector has, further, a relatively large constructional size.